The Ivory Coast defender gifted Victor Anichebe a leveller for the Baggies in the 67th minute, allowing him to cancel out Daniel Sturridge's 24th-minute opener, but Rodgers refused to place fault on his centre-back.
"Defensively, we were very, very good," he told Sky Sports.
"I'll never criticise players for trying to play football but Kolo probably shouldn't have received the ball under pressure and his pass was misplaced.
"But for me, it's the bravest place on the field as we look to build our play from behind. That has won us many games this season.
"We like to build the game and construct play from behind and sometimes it will cost you and today was unfortunately one of those days.
"Kolo Toure has been brilliant since he's been here. He's been a real leader, an outstanding professional and, unfortunately, it was a mistake."
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